Investigation On Types Of Errors In "Linear Function" Problem Solving By Junior Grade 3 Students

Function contains abundant mathematical thought and is an important material to cultivate students' mathematical ability.But for the middle school students who have first contact function,they also exposed a series of errors in solving problems.Based on the classification theory of Dai Zaiying's problem-solving errors,this paper classifies the junior grade 3 students' "Linear function" problem-solving errors into intellectual errors,logical errors,strategic errors,interfering errors and negligent errors.Hope to help teachers and students to understand and use mistakes correctly through collecting,analyzing and attributing the problem solving errors of "Linear function".This paper will focus on the following three questions:(1)What types of mistakes are there in the process of solving the problem of "Linear function" ?(2)What are the reasons for the error in solving the problem of "Linear function" ?(3)What are the teaching countermeasure to reduce the problem solving error of "Linear function" ?This paper selects some junior grade 3 students and four front-line teachers from A middle school in a city as the research objects,and uses the methods of literature research,test survey and interview to collect abundant original data and text materials.Using SPSS24.0 and Excel software to sort out and analyze the data,it is concluded that the types of errors in "Linear function" learning process of junior grade 3 students are as follows:(1)Intellectual errors:unclear concept;conversion of the three expression forms of the function is not smooth;unequal transformation of an equation;(2)Logical errors:insufficient mining of implicit information;poor integration of graph and text information;determining function relationship is blocked;ignore the condition that the coefficient of the first term is not 0;(3)Strategic errors: single method of solving problems;loose connection between knowledge;(4)Interference error:negative transfer of knowledge and experience;(5)Negligent error: calculation error;transcription error;nonstandard drawing.The specific reasons for the "Linear function" problem solving error of junior grade 3students are as follows:(1)internal reasons: the corresponding knowledge structure is not complete enough;Problem-solving thinking solidified;Bad study habits;Lack of error analysis awareness.(2)External causes: teachers focus excessively on the concept itself;Lack of awareness of cultivating mathematical ability.Comprehensive materials,for teachers and students respectively put forward the following countermeasures:(1)teachers teaching countermeasures: Provide counter-example teaching;Emphasis on concept formation;Analogical material,;Strengthen the training of comprehensive questions;Organize teachers to prepare lessons collectively;Pay attention to the training of problem solving methods;Appropriate use of multimedia;Pay attention to the cultivation of learning habits;.(2)Countermeasures for students: Choose appropriate learning strategies;Develop good study habits;Summarize and summarize the questions.